Dear Jiqiang Li, 1) If you compute <psi_i|psi_j> at the same point then the result is delta_ij. If the bands are different at the same kpoint then you will get zero for this value.
If you are outputting the wavefunction at <psi_1|psi_2> and getting a complex number other than 0+0i or some other sufficiently small number I suspect you are doing it incorrectly. For example when I compute these values I get a value on the order of 10^-17. Perhaps if you modified your wavefunction. It should instead read psi_j(k,r) = sum_G C_j,G(k) exp(-(G+k)*r)) as a plane wave description would generally require. If you work it out by hand then the overlap will be <psi_i|psi_j> = sum_G C*_i,G(k) C_j,G(k) My suspicion is that you are doing something incorrectly. 2) In my experience no, not unless you force the Gamma point only calculation. I apologize if the notation here doesn't quite work out so well. Writing equations in text like this does not work well. Robert Hembree Quantum Theory project. From: pw_forum-boun...@pwscf.org [mailto:pw_forum-boun...@pwscf.org] On Behalf Of Jiqiang Li Sent: Friday, April 17, 2015 12:59 AM To: pw_forum Subject: [Pw_forum] About wavefunction Dear all, 1. In Quantum Espresso, do wavefunction in real space form at the same k point share the same phase? i.e., psi_1(r) = A(r)exp(ikr) and psi_2(r)=B(r)exp(ikr), psi_1 and psi_2 belong to different bands at same k point. If so, we should find the vaule < psi_1 | psi_2 > = A(r)exp(-ikr)*B(r)exp(ikr)=A(r)B(r), which is a series of real number. However, I output the wavefunctions and found < psi_1 | psi_2 > was also a complex number. Could you tell me the reason? 2. Is the wavefunction in real space form at Gamma point a series of real number? ( not only for the gamma point only calculation) Thanks for your consideration! Best regards! Jiqiang Li Fudan University, China _____
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